## new methode for finding M(p) ?

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• Hello , I have found a relation for Mersenne primes. Perhaps is it know ?! R=(2*M(p)-2)/3=(T^2 mod M(p)) The problem is,how can I proof that exist a number T
Message 1 of 3 , Mar 23, 2008
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Hello , I have found a relation for Mersenne primes.
Perhaps is it know ?!

R=(2*M(p)-2)/3=(T^2 mod M(p))

The problem is,how can I proof that exist a number T
where T^2 mod M(p) = R. T is >= R

Example:

M(13)=8191
R=5460
we found T=5929

The idea is a consequence of the Lucas Lehmer Test.

regards

Norman

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• T is not =R. We find for M(5) T=12,19 M(7) T=46,81 M(11) no T so that T^2 mod 2047 = 1364 M(13) T=2262,5929 .... N.L. Lesen Sie Ihre E-Mails jetzt einfach von
Message 2 of 3 , Mar 23, 2008
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T is not >=R.

We find for
M(5) T=12,19
M(7) T=46,81
M(11) no T so that T^2 mod 2047 = 1364
M(13) T=2262,5929
....

N.L.

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• ... if R=(2*Mp-2)/3=((T^2) mod Mp), then... ... (it s a plausible idea), but if it works?? it s better than LL I can determine the exact T(sub k) to use in
Message 3 of 3 , Mar 25, 2008
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--- In primenumbers@yahoogroups.com, Norman Luhn <nluhn@...> wrote:
>
> Hello , I have found a relation for Mersenne primes.
> Perhaps is it know(n) ?! (probably not!)
>
if R=(2*Mp-2)/3=((T^2) mod Mp), then...
>
(it's a plausible idea), but if it works?? it's better than LL

I can determine the exact T(sub k) to use in this test.
e.g. #1
Suppose that Mp= 7, and p= 3;
R = (2*7 -2)/3 =4 == ((2^2) mod 7) == 4; M3 is prime!
T was chosen by taking R/2 = 4/2 = 2 = T(1);
..2.....4....6...8... and so on...
T(1)...(2)..(3).(4)...
where k= floor[(p+1)/2 -1] = floor[(3+1)/2 -1] = 1; p= 3 from M(3).

e.g #2
Suppose that Mp= 31, and p= 5;
R = (2*31 -2)/3 =20 == ((2^12) mod 31) == 20; M5 is prime!
T was chosen by taking R/2 = 20/2 = 10 = T(1); but k equals 2(below)
.10...12....14... and so on...
T(1)..(2)...(3) ...
where k= floor[(p+1)/2] -1 = floor[(5+1)/2] -1 = 2; p= 5 from M5.

Try another Norm... and see if I'm right. Imagine... a single test
to determine the primality of Mp's! We can call it the Luhn-Bouris
test for Mersennes. It can always be confirmed using the LL-test.
Bill Bouris

>
> Example:
>
> M(13)=8191
> R=5460
> we found T=5929
>
> The idea is a consequence of the Lucas Lehmer Test.
>
>
> regards
>
> Norman
>
>
>
> Lesen Sie Ihre E-Mails jetzt einfach von unterwegs.
> www.yahoo.de/go
>
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